变系数三阶周期边值问题的正解(英文)

Positive Solutions of Third-Order Periodic Boundary Value Problems with Variable Coefficient

研究了变系数非线性三阶周期边值问题的正解.非线性项可以关于空间变元奇异.利用适当的变换此问题被转换为一个Hammerstein积分方程,利用锥上的Guo-Krasno-selski不动点定理获得了1～2个正解的存在性.

The positive solutions of a nonlinear third-order periodic boundary value problem with variable coefficient are studied.The nonlinear term may be singular with respect to the space variable.By making use of a suitable transformation,the problem is transformed into a Hammerstein integral equation.By applying Guo-Krasnosel'skii fixed point theorem on cone,the existence of one and two po sitive solutions is proved.